private void CalculateInitialConfigurationData(IElement element)
{
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
Matrix[] BL13_hexa;
BL13_hexa = GetBL13Hexa(shapeFunctionNaturalDerivatives);
Matrix[] BNL1_hexa;
ox_i = new double[8][];
tu_i = new double[8][];
(Matrix[] J_0inv_hexa, double[] detJ_0) = JacobianHexa8Reverse.GetJ_0invHexaAndDetJ_0(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
integrationCoeffs = new double[nGaussPoints];
BNL1_hexa = GetBNL1_hexa(J_0inv_hexa);
for (int j = 0; j < 8; j++)
{
ox_i[j] = new double[] { element.Nodes[j].X, element.Nodes[j].Y, element.Nodes[j].Z, };
}
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrationCoeffs[gpoint] = detJ_0[gpoint] * QuadratureForStiffness.IntegrationPoints[gpoint].Weight;
}
tu_i = new double[8][];
//GLvec = new double[nGaussPoints][]; //MS
//GLvec_last_converged = new double[nGaussPoints][];
DefGradVec = new double[nGaussPoints][];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
//GLvec[gpoint] = new double[6]; //MS
//GLvec_last_converged[gpoint] = new double[6];
DefGradVec[gpoint] = new double[9];
}
for (int k = 0; k < 8; k++)
{
tu_i[k] = new double[3];
}
isInitialized = true;
}
private void CalculateInitialConfigurationData(IElement element)
{
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
Matrix[] bl13Matrices;
bl13Matrices = Getbl13DeformationMatrices(shapeFunctionNaturalDerivatives);
Matrix[] bnl1Matrices;
initialCoordinates = new double[8][];
totalDisplacements = new double[8][];
(Matrix[] jacobianInverse, double[] jacobianDeterminants) = JacobianHexa8Reverse.GetJ_0invHexaAndjacobianDeterminants(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
integrationCoeffs = new double[nGaussPoints];
bnl1Matrices = GetAuxilliaryDeformationbnl1Matrices(jacobianInverse);
for (int j = 0; j < 8; j++)
{
initialCoordinates[j] = new double[] { element.Nodes[j].X, element.Nodes[j].Y, element.Nodes[j].Z, };
}
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrationCoeffs[gpoint] = jacobianDeterminants[gpoint] * QuadratureForStiffness.IntegrationPoints[gpoint].Weight;
}
totalDisplacements = new double[8][];
strainsVec = new double[nGaussPoints][];
strainsVec_last_converged = new double[nGaussPoints][];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
strainsVec[gpoint] = new double[6];
strainsVec_last_converged[gpoint] = new double[6];
}
for (int k = 0; k < 8; k++)
{
totalDisplacements[k] = new double[3];
}
isInitialized = true;
}
private void CalculateStrains(double[] localdisplacements, IElement element, double[][] tx_i)
{
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] J_0inv_hexa, double[] detJ_0) = JacobianHexa8Reverse.GetJ_0invHexaAndDetJ_0(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
//TODO: possibility of caching ll1_hexa or J_0inv
Matrix[] DGtr = new Matrix[nGaussPoints];
//Matrix[] GL = new Matrix[nGaussPoints]; //MS
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
DGtr[npoint] = Matrix.CreateZero(3, 3);
//GL[npoint] = Matrix.CreateZero(3, 3); //MS
}
Matrix[] J_1 = JacobianHexa8Reverse.Get_J_1(nGaussPoints, tx_i, shapeFunctionNaturalDerivatives);
//
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
//
DGtr[npoint] = J_0inv_hexa[npoint] * J_1[npoint];
DefGradVec[npoint] = new double[9] {
DGtr[npoint][0, 0], DGtr[npoint][1, 1], DGtr[npoint][2, 2], DGtr[npoint][1, 0], DGtr[npoint][2, 1], DGtr[npoint][0, 2], DGtr[npoint][2, 0], DGtr[npoint][0, 1], DGtr[npoint][1, 2],
}; //MS
////
//GL[npoint] = DGtr[npoint] * DGtr[npoint].Transpose();
//for (int m = 0; m < 3; m++)
//{
// GL[npoint][m, m] += -1;
//}
//GL[npoint].ScaleIntoThis(0.5);
////
//for (int m = 0; m < 3; m++)
//{
// GLvec[npoint][m] = GL[npoint][m, m];
//}
//GLvec[npoint][3] = 2 * GL[npoint][0, 1];
//GLvec[npoint][4] = 2 * GL[npoint][1, 2];
//GLvec[npoint][5] = 2 * GL[npoint][2, 0];
}
}
private void CalculateStrains(double[] localdisplacements, IElement element, double[][] deformedCoordinates)
{
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] jacobianInverse, double[] jacobianDeterminants) = JacobianHexa8Reverse.GetJ_0invHexaAndjacobianDeterminants(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
//TODO: possibility of caching shapeFunctionNaturalDerivatives or J_0inv
Matrix[] deformationGradientsTransposed = new Matrix[nGaussPoints];
Matrix[] GL = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
deformationGradientsTransposed[npoint] = Matrix.CreateZero(3, 3);
GL[npoint] = Matrix.CreateZero(3, 3);
}
Matrix[] jacobiansDeformedMatrices = JacobianHexa8Reverse.Get_jacobiansDeformedMatrices(nGaussPoints, deformedCoordinates, shapeFunctionNaturalDerivatives);
//
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
//
deformationGradientsTransposed[npoint] = jacobianInverse[npoint] * jacobiansDeformedMatrices[npoint];
//
GL[npoint] = deformationGradientsTransposed[npoint] * deformationGradientsTransposed[npoint].Transpose();
for (int m = 0; m < 3; m++)
{
GL[npoint][m, m] += -1;
}
GL[npoint].ScaleIntoThis(0.5);
//
for (int m = 0; m < 3; m++)
{
strainsVec[npoint][m] = GL[npoint][m, m];
}
strainsVec[npoint][3] = 2 * GL[npoint][0, 1];
strainsVec[npoint][4] = 2 * GL[npoint][1, 2];
strainsVec[npoint][5] = 2 * GL[npoint][2, 0];
}
}
private Matrix UpdateKmatrices(IElement element)
{
Matrix k_element = Matrix.CreateZero(24, 24);
// initialization of matrices that are not cached currently
double[][] integrCoeff_Spkvec = new double[nGaussPoints][];
Matrix[] BL = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrCoeff_Spkvec[gpoint] = new double[6];
BL[gpoint] = Matrix.CreateZero(6, 24);
}
Matrix ll2 = Matrix.CreateZero(8, 3);
for (int m = 0; m < 8; m++)
{
for (int n = 0; n < 3; n++)
{
ll2[m, n] = tu_i[m][n];
}
}
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] J_0inv_hexa, double[] detJ_0) = JacobianHexa8Reverse.GetJ_0invHexaAndDetJ_0(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
Matrix[] BL13_hexa;
BL13_hexa = GetBL13Hexa(shapeFunctionNaturalDerivatives);
Matrix[] BL11a_hexa; // dimension: gpoints
Matrix[] BL12_hexa;
Matrix[] BL01_hexa;
BL11a_hexa = GetBL11a_hexa(J_0inv_hexa);
BL12_hexa = GetBL12_hexa(J_0inv_hexa);
BL01_hexa = GetBL01_hexa(J_0inv_hexa);
Matrix[] BL11 = new Matrix[nGaussPoints];
Matrix[] BL1112sun01_hexa = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
BL11[npoint] = Matrix.CreateZero(6, 9);
BL1112sun01_hexa[npoint] = Matrix.CreateZero(6, 9); //TODO this may be unnescessary
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
//
integrCoeff_Spkvec[npoint] = materialsAtGaussPoints[npoint].Stresses.Scale(integrationCoeffs[npoint]);
//
Matrix l_cyrcumflex = Matrix.CreateZero(3, 3);
l_cyrcumflex = shapeFunctionNaturalDerivatives[npoint] * ll2;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 3; n++)
{
for (int p = 0; p < 3; p++)
{
BL11[npoint][m, n] += BL11a_hexa[npoint][m, p] * l_cyrcumflex[p, n];
BL11[npoint][m, 3 + n] += BL11a_hexa[npoint][m, 3 + p] * l_cyrcumflex[p, n];
BL11[npoint][m, 6 + n] += BL11a_hexa[npoint][m, 6 + p] * l_cyrcumflex[p, n];
}
}
}
//
BL1112sun01_hexa[npoint] = BL11[npoint] * BL12_hexa[npoint];
BL1112sun01_hexa[npoint].AddIntoThis(BL01_hexa[npoint]);
//
BL[npoint] = BL1112sun01_hexa[npoint] * BL13_hexa[npoint];
}
// TODO: BL and above calculations can cached from calculate forces method
Matrix[] BNL1_hexa;
Matrix[] BNL_hexa;
BNL1_hexa = GetBNL1_hexa(J_0inv_hexa);
BNL_hexa = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
BNL_hexa[gpoint] = Matrix.CreateZero(9, 24); //todo this may be unnescessary
BNL_hexa[gpoint] = BNL1_hexa[gpoint] * BL13_hexa[gpoint];
}
Matrix[] integrCoeff_Spk = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
integrCoeff_Spk[npoint] = Matrix.CreateZero(3, 3);
}
Matrix[] kl_ = new Matrix[nGaussPoints + 1];
Matrix[] knl_ = new Matrix[nGaussPoints + 1];
for (int npoint = 0; npoint < nGaussPoints + 1; npoint++)
{
kl_[npoint] = Matrix.CreateZero(24, 24);
knl_[npoint] = Matrix.CreateZero(24, 24);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
Matrix integrCoeff_SPK_epi_BNL_hexa = Matrix.CreateZero(9, 24); //TODO
Matrix integrCoeff_cons_disp = Matrix.CreateZero(6, 6); //TODO
Matrix integrCoeff_cons_disp_epi_BL = Matrix.CreateZero(6, 24); //TODO
//
integrCoeff_Spk[npoint][0, 0] = integrCoeff_Spkvec[npoint][0];
integrCoeff_Spk[npoint][0, 1] = integrCoeff_Spkvec[npoint][3];
integrCoeff_Spk[npoint][0, 2] = integrCoeff_Spkvec[npoint][5];
integrCoeff_Spk[npoint][1, 0] = integrCoeff_Spkvec[npoint][3];
integrCoeff_Spk[npoint][1, 1] = integrCoeff_Spkvec[npoint][1];
integrCoeff_Spk[npoint][1, 2] = integrCoeff_Spkvec[npoint][4];
integrCoeff_Spk[npoint][2, 0] = integrCoeff_Spkvec[npoint][5];
integrCoeff_Spk[npoint][2, 1] = integrCoeff_Spkvec[npoint][4];
integrCoeff_Spk[npoint][2, 2] = integrCoeff_Spkvec[npoint][2];
//
IMatrixView consDisp = materialsAtGaussPoints[npoint].ConstitutiveMatrix;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 6; n++)
{
integrCoeff_cons_disp[m, n] = integrationCoeffs[npoint] * consDisp[m, n];
}
}
//
integrCoeff_cons_disp_epi_BL = integrCoeff_cons_disp * BL[npoint];
//
kl_[npoint] = BL[npoint].Transpose() * integrCoeff_cons_disp_epi_BL;
//
for (int m = 0; m < 3; m++) // 3x24 dimensions
{
for (int n = 0; n < 24; n++)
{
for (int p = 0; p < 3; p++)
{
integrCoeff_SPK_epi_BNL_hexa[m, n] += integrCoeff_Spk[npoint][m, p] * BNL_hexa[npoint][p, n];
integrCoeff_SPK_epi_BNL_hexa[3 + m, n] += integrCoeff_Spk[npoint][m, p] * BNL_hexa[npoint][3 + p, n];
integrCoeff_SPK_epi_BNL_hexa[6 + m, n] += integrCoeff_Spk[npoint][m, p] * BNL_hexa[npoint][6 + p, n];
}
}
}
//
knl_[npoint] = BNL_hexa[npoint].Transpose() * integrCoeff_SPK_epi_BNL_hexa;
}
// Add contributions of each gp on the total element stiffness matrix k_element
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
for (int m = 0; m < 24; m++)
{
for (int n = 0; n < 24; n++)
{
kl_[nGaussPoints][m, n] += kl_[npoint][m, n];
knl_[nGaussPoints][m, n] += knl_[npoint][m, n];
}
}
}
for (int m = 0; m < 24; m++)
{
for (int n = 0; n < 24; n++)
{
k_element[m, n] = kl_[nGaussPoints][m, n] + knl_[nGaussPoints][m, n];
}
}
return(k_element);
}
private double[] UpdateForces(IElement element)
{
//TODO: the gauss point loop should be the outer one
// Matrices that are not currently cached are calculated here.
Matrix ll2 = Matrix.CreateZero(8, 3);
for (int m = 0; m < 8; m++)
{
for (int n = 0; n < 3; n++)
{
ll2[m, n] = tu_i[m][n];
}
}
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] J_0inv_hexa, double[] detJ_0) = JacobianHexa8Reverse.GetJ_0invHexaAndDetJ_0(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
Matrix[] BL13_hexa;
BL13_hexa = GetBL13Hexa(shapeFunctionNaturalDerivatives);
Matrix[] BL11a_hexa; // dimension number of gpoints
Matrix[] BL12_hexa;
Matrix[] BL01_hexa;
BL11a_hexa = GetBL11a_hexa(J_0inv_hexa);
BL12_hexa = GetBL12_hexa(J_0inv_hexa);
BL01_hexa = GetBL01_hexa(J_0inv_hexa);
//INITIALIZATION of MAtrixes that are currently not cached
double[][] integrCoeff_Spkvec = new double[nGaussPoints][];
Matrix[] BL = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrCoeff_Spkvec[gpoint] = new double[6];
BL[gpoint] = Matrix.CreateZero(6, 24);
}
double[][] fxk1 = new double[nGaussPoints + 1][];
for (int npoint = 0; npoint < nGaussPoints + 1; npoint++)
{
fxk1[npoint] = new double[24];
}
Matrix[] BL11 = new Matrix[nGaussPoints];
Matrix[] BL1112sun01_hexa = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
BL11[npoint] = Matrix.CreateZero(6, 9);
BL1112sun01_hexa[npoint] = Matrix.CreateZero(6, 9);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
integrCoeff_Spkvec[npoint] = materialsAtGaussPoints[npoint].Stresses.Scale(integrationCoeffs[npoint]);
//
Matrix l_cyrcumflex = Matrix.CreateZero(3, 3);
l_cyrcumflex = shapeFunctionNaturalDerivatives[npoint] * ll2;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 3; n++)
{
for (int p = 0; p < 3; p++)
{
BL11[npoint][m, n] += BL11a_hexa[npoint][m, p] * l_cyrcumflex[p, n];
BL11[npoint][m, 3 + n] += BL11a_hexa[npoint][m, 3 + p] * l_cyrcumflex[p, n];
BL11[npoint][m, 6 + n] += BL11a_hexa[npoint][m, 6 + p] * l_cyrcumflex[p, n];
}
}
}
//
BL1112sun01_hexa[npoint] = BL11[npoint] * BL12_hexa[npoint];
BL1112sun01_hexa[npoint].AddIntoThis(BL01_hexa[npoint]);
//
BL[npoint] = BL1112sun01_hexa[npoint] * BL13_hexa[npoint];
//
fxk1[npoint] = BL[npoint].Multiply(integrCoeff_Spkvec[npoint], true);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
fxk1[nGaussPoints].AddIntoThis(fxk1[npoint]);
}
return(fxk1[nGaussPoints]);
}
private Matrix UpdateKmatrices(IElement element)
{
Matrix elementStiffnessMatrix = Matrix.CreateZero(24, 24);
// initialization of matrices that are not cached currently
double[][] integrCoeffsTimesStresses = new double[nGaussPoints][];
Matrix[] BL = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrCoeffsTimesStresses[gpoint] = new double[6];
BL[gpoint] = Matrix.CreateZero(6, 24);
}
Matrix ll2 = Matrix.CreateZero(8, 3);
for (int m = 0; m < 8; m++)
{
for (int n = 0; n < 3; n++)
{
ll2[m, n] = totalDisplacements[m][n];
}
}
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] jacobianInverse, double[] jacobianDeterminants) = JacobianHexa8Reverse.GetJ_0invHexaAndjacobianDeterminants(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
Matrix[] bl13Matrices;
bl13Matrices = Getbl13DeformationMatrices(shapeFunctionNaturalDerivatives);
Matrix[] bl11aMatrices; // dimension: gpoints
Matrix[] bl12Marices;
Matrix[] bl01Matrices;
bl11aMatrices = Getbl11aDeformationMatrices(jacobianInverse);
bl12Marices = GetBL12DeformationMatrices(jacobianInverse);
bl01Matrices = Getbl01MDeformationMatrices(jacobianInverse);
Matrix[] BL11 = new Matrix[nGaussPoints];
Matrix[] bL1112Plus01Matrices = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
BL11[npoint] = Matrix.CreateZero(6, 9);
bL1112Plus01Matrices[npoint] = Matrix.CreateZero(6, 9); //TODO this may be unnescessary
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
//
integrCoeffsTimesStresses[npoint] = materialsAtGaussPoints[npoint].Stresses.Scale(integrationCoeffs[npoint]);
//
Matrix lcyrcumflex = Matrix.CreateZero(3, 3);
lcyrcumflex = shapeFunctionNaturalDerivatives[npoint].Transpose() * ll2;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 3; n++)
{
for (int p = 0; p < 3; p++)
{
BL11[npoint][m, n] += bl11aMatrices[npoint][m, p] * lcyrcumflex[p, n];
BL11[npoint][m, 3 + n] += bl11aMatrices[npoint][m, 3 + p] * lcyrcumflex[p, n];
BL11[npoint][m, 6 + n] += bl11aMatrices[npoint][m, 6 + p] * lcyrcumflex[p, n];
}
}
}
//
bL1112Plus01Matrices[npoint] = BL11[npoint] * bl12Marices[npoint];
bL1112Plus01Matrices[npoint].AddIntoThis(bl01Matrices[npoint]);
//
BL[npoint] = bL1112Plus01Matrices[npoint] * bl13Matrices[npoint];
}
// TODO: BL and above calculations can cached from calculate forces method
Matrix[] bnl1Matrices;
Matrix[] bnlMatrices;
bnl1Matrices = GetAuxilliaryDeformationbnl1Matrices(jacobianInverse);
bnlMatrices = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
bnlMatrices[gpoint] = Matrix.CreateZero(9, 24); //todo this may be unnescessary
bnlMatrices[gpoint] = bnl1Matrices[gpoint] * bl13Matrices[gpoint];
}
Matrix[] integrCoeff_Spk = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
integrCoeff_Spk[npoint] = Matrix.CreateZero(3, 3);
}
Matrix[] kl_ = new Matrix[nGaussPoints + 1];
Matrix[] knl_ = new Matrix[nGaussPoints + 1];
for (int npoint = 0; npoint < nGaussPoints + 1; npoint++)
{
kl_[npoint] = Matrix.CreateZero(24, 24);
knl_[npoint] = Matrix.CreateZero(24, 24);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
Matrix integrCoeff_SPK_epi_bnlMatrices = Matrix.CreateZero(9, 24); //TODO
Matrix integrCoeff_cons_disp = Matrix.CreateZero(6, 6); //TODO
Matrix integrCoeff_cons_disp_epi_BL = Matrix.CreateZero(6, 24); //TODO
//
integrCoeff_Spk[npoint][0, 0] = integrCoeffsTimesStresses[npoint][0];
integrCoeff_Spk[npoint][0, 1] = integrCoeffsTimesStresses[npoint][3];
integrCoeff_Spk[npoint][0, 2] = integrCoeffsTimesStresses[npoint][5];
integrCoeff_Spk[npoint][1, 0] = integrCoeffsTimesStresses[npoint][3];
integrCoeff_Spk[npoint][1, 1] = integrCoeffsTimesStresses[npoint][1];
integrCoeff_Spk[npoint][1, 2] = integrCoeffsTimesStresses[npoint][4];
integrCoeff_Spk[npoint][2, 0] = integrCoeffsTimesStresses[npoint][5];
integrCoeff_Spk[npoint][2, 1] = integrCoeffsTimesStresses[npoint][4];
integrCoeff_Spk[npoint][2, 2] = integrCoeffsTimesStresses[npoint][2];
//
IMatrixView consDisp = materialsAtGaussPoints[npoint].ConstitutiveMatrix;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 6; n++)
{
integrCoeff_cons_disp[m, n] = integrationCoeffs[npoint] * consDisp[m, n];
}
}
//
integrCoeff_cons_disp_epi_BL = integrCoeff_cons_disp * BL[npoint];
//
kl_[npoint] = BL[npoint].Transpose() * integrCoeff_cons_disp_epi_BL;
//
for (int m = 0; m < 3; m++) // 3x24 dimensions
{
for (int n = 0; n < 24; n++)
{
for (int p = 0; p < 3; p++)
{
integrCoeff_SPK_epi_bnlMatrices[m, n] += integrCoeff_Spk[npoint][m, p] * bnlMatrices[npoint][p, n];
integrCoeff_SPK_epi_bnlMatrices[3 + m, n] += integrCoeff_Spk[npoint][m, p] * bnlMatrices[npoint][3 + p, n];
integrCoeff_SPK_epi_bnlMatrices[6 + m, n] += integrCoeff_Spk[npoint][m, p] * bnlMatrices[npoint][6 + p, n];
}
}
}
//
knl_[npoint] = bnlMatrices[npoint].Transpose() * integrCoeff_SPK_epi_bnlMatrices;
}
// Add contributions of each gp on the total element stiffness matrix elementStiffnessMatrix
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
for (int m = 0; m < 24; m++)
{
for (int n = 0; n < 24; n++)
{
kl_[nGaussPoints][m, n] += kl_[npoint][m, n];
knl_[nGaussPoints][m, n] += knl_[npoint][m, n];
}
}
}
for (int m = 0; m < 24; m++)
{
for (int n = 0; n < 24; n++)
{
elementStiffnessMatrix[m, n] = kl_[nGaussPoints][m, n] + knl_[nGaussPoints][m, n];
}
}
return(elementStiffnessMatrix);
}
private double[] UpdateForces(IElement element)
{
//TODO: the gauss point loop should be the outer one
// Matrices that are not currently cached are calculated here.
Matrix ll2 = Matrix.CreateZero(8, 3);
for (int m = 0; m < 8; m++)
{
for (int n = 0; n < 3; n++)
{
ll2[m, n] = totalDisplacements[m][n];
}
}
IReadOnlyList <Matrix> shapeFunctionNaturalDerivatives;
shapeFunctionNaturalDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] jacobianInverse, double[] jacobianDeterminants) = JacobianHexa8Reverse.GetJ_0invHexaAndjacobianDeterminants(
shapeFunctionNaturalDerivatives, element.Nodes, nGaussPoints);
Matrix[] bl13Matrices;
bl13Matrices = Getbl13DeformationMatrices(shapeFunctionNaturalDerivatives);
Matrix[] bl11aMatrices; // dimension number of gpoints
Matrix[] bl12Marices;
Matrix[] bl01Matrices;
bl11aMatrices = Getbl11aDeformationMatrices(jacobianInverse);
bl12Marices = GetBL12DeformationMatrices(jacobianInverse);
bl01Matrices = Getbl01MDeformationMatrices(jacobianInverse);
//INITIALIZATION of MAtrixes that are currently not cached
double[][] integrCoeffsTimesStresses = new double[nGaussPoints][];
Matrix[] BL = new Matrix[nGaussPoints];
for (int gpoint = 0; gpoint < nGaussPoints; gpoint++)
{
integrCoeffsTimesStresses[gpoint] = new double[6];
BL[gpoint] = Matrix.CreateZero(6, 24);
}
double[][] forces = new double[nGaussPoints + 1][];
for (int npoint = 0; npoint < nGaussPoints + 1; npoint++)
{
forces[npoint] = new double[24];
}
Matrix[] BL11 = new Matrix[nGaussPoints];
Matrix[] bL1112Plus01Matrices = new Matrix[nGaussPoints];
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
BL11[npoint] = Matrix.CreateZero(6, 9);
bL1112Plus01Matrices[npoint] = Matrix.CreateZero(6, 9);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
integrCoeffsTimesStresses[npoint] = materialsAtGaussPoints[npoint].Stresses.Scale(integrationCoeffs[npoint]);
//
Matrix lcyrcumflex = Matrix.CreateZero(3, 3);
lcyrcumflex = shapeFunctionNaturalDerivatives[npoint].Transpose() * ll2;
for (int m = 0; m < 6; m++)
{
for (int n = 0; n < 3; n++)
{
for (int p = 0; p < 3; p++)
{
BL11[npoint][m, n] += bl11aMatrices[npoint][m, p] * lcyrcumflex[p, n];
BL11[npoint][m, 3 + n] += bl11aMatrices[npoint][m, 3 + p] * lcyrcumflex[p, n];
BL11[npoint][m, 6 + n] += bl11aMatrices[npoint][m, 6 + p] * lcyrcumflex[p, n];
}
}
}
//
bL1112Plus01Matrices[npoint] = BL11[npoint] * bl12Marices[npoint];
bL1112Plus01Matrices[npoint].AddIntoThis(bl01Matrices[npoint]);
//
BL[npoint] = bL1112Plus01Matrices[npoint] * bl13Matrices[npoint];
//
forces[npoint] = BL[npoint].Multiply(integrCoeffsTimesStresses[npoint], true);
}
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
forces[nGaussPoints].AddIntoThis(forces[npoint]);
}
return(forces[nGaussPoints]);
}
